Boolean Functions for Homomorphic-Friendly Stream Ciphers

2019 ◽  
pp. 166-182
Author(s):  
Claude Carlet ◽  
Pierrick Méaux
Keyword(s):  
Boolean Functions ◽  
Stream Ciphers

Boolean Functions for Stream Ciphers

2019 ◽  
Author(s):  
Oleksandr Potii ◽  
Nikolay Poluyanenko ◽  
Anna Petrenko ◽  
Oleg Pidkhomnyi ◽  
Serhii Florov ◽  
...  
Keyword(s):  
Boolean Functions ◽  
Stream Ciphers

A CLASS OF 1-RESILIENT BOOLEAN FUNCTIONS WITH OPTIMAL ALGEBRAIC IMMUNITY AND GOOD BEHAVIOR AGAINST FAST ALGEBRAIC ATTACKS

2014 ◽  
Vol 25 (06) ◽  
pp. 763-780 ◽  
Author(s):  
DENG TANG ◽  
CLAUDE CARLET ◽  
XIAOHU TANG
Keyword(s):  
Boolean Functions ◽  
Algebraic Degree ◽  
Stream Ciphers ◽  
Algebraic Immunity ◽  
Infinite Class ◽  
Algebraic Attacks ◽  
Correlation Attack ◽  
Fast Algebraic Attacks ◽  
First Time ◽  
Class Of Functions

Recently, Tang, Carlet and Tang presented a combinatorial conjecture about binary strings, allowing proving that all balanced functions in some infinite class they introduced have optimal algebraic immunity. Later, Cohen and Flori completely proved that the conjecture is true. These functions have good (provable or at least observable) cryptographic properties but they are not 1-resilient, which represents a drawback for their use as filter functions in stream ciphers. We propose a construction of an infinite class of 1-resilient Boolean functions with optimal algebraic immunity by modifying the functions in this class. The constructed functions have optimal algebraic degree, that is, meet the Siegenthaler bound, and high nonlinearity. We prove a lower bound on their nonlinearity, but as for the Carlet-Feng functions and for the functions mentioned above, this bound is not enough for ensuring a nonlinearity sufficient for allowing resistance to the fast correlation attack. Nevertheless, as for previously found functions with the same features, there is a gap between the bound that we can prove and the actual values computed for small numbers of variables. Our computations show that the functions in this class have very good nonlinearity and also good immunity to fast algebraic attacks. This is the first time that an infinite class of functions gathers all of the main criteria allowing these functions to be used as filters in stream ciphers.

Generic cryptographic weakness of k-normal Boolean functions in certain stream ciphers and cryptanalysis of grain-128

2012 ◽  
Vol 65 (2) ◽  
pp. 205-227 ◽  
Author(s):  
Miodrag J. Mihaljević ◽  
Sugata Gangopadhyay ◽  
Goutam Paul ◽  
Hideki Imai
Keyword(s):  
Boolean Functions ◽  
Stream Ciphers

Construction of Boolean Function with Maximum Algebraic Immunity

2012 ◽  
Vol 546-547 ◽  
pp. 387-392
Author(s):  
Xiao Wen Xiong ◽  
Ai Guo Wei ◽  
Kai Yin
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Stream Ciphers ◽  
Algebraic Immunity ◽  
Algebraic Attacks ◽  
Survey Paper

To resist algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In recent years, several constructions of Boolean functions with maximum algebraic immunity (MAI) have been investigated. In this survey paper, we review the recent constructions of Boolean functions with MAI, and classify those into several different classes by the construction idea. Further, we also present some results and developments of these methods, including some results of the authors.

scholarly journals On an improved correlation analysis of stream ciphers using multi-output Boolean functions and the related generalized notion of nonlinearity

2008 ◽  
Vol 2 (2) ◽  
pp. 201-221 ◽  
Author(s):  
Claude Carlet ◽  
◽  
Khoongming Khoo ◽  
Chu-Wee Lim ◽  
Chuan-Wen Loe ◽  
...  
Keyword(s):  
Correlation Analysis ◽  
Boolean Functions ◽  
Stream Ciphers

Noise Sensitivity of Boolean Functions and Percolation

2015 ◽  
Author(s):  
Christophe Garban ◽  
Jeffrey E. Steif
Keyword(s):  
Boolean Functions ◽  
Noise Sensitivity
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